Hitting distributions domination and subordinate resolvents; an analytic approach

• Autorzy: Nicu Boboc , Gheorghe Bucur
• Języki publikacji: EN

Abstrakty

EN

We give an analytic version of the well known Shih's theorem concerning the Markov processes whose hitting distributions are dominated by those of a given process. The treatment is purely analytic, completely different from Shih's arguments and improves essentially his result (in the case when the given processes are transient

Słowa kluczowe

EN

Subordinate resolvents; hitting distribution; Markov process; excessive function; 31D05; 60J45; 60J35

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2006
• Tom: 4
• Numer: 1
• Strony: 138-162

Daty

wydano

2006-03-01

online

2006-03-01

Twórcy

autor

Nicu Boboc

• University of Bucharest,

autor

Gheorghe Bucur

Bibliografia

• [1] H. Ben Saad: Généralisation des noyaux V het applications, Lecture Notes in Math, Vol. 196, Springer Verlag, (1984), pp. 14-39.
• [2] L. Beznea and N. Boboc: “Excessive functions and excessive measures: Hunt's theorem on balayages, quasi-continuity”, In: Classical and Modern Potential Theory and Appl., NATO ASI Series C, Vol. 430, Kluwer Acad. Publish., 1994, pp. 71–92.
• [3] L. Beznea and N. Boboc: “Kuran's regularity criterion and localization in excessive structures”, Bull. London Math. Soc., Vol. 28, (1996), pp. 273–282.
• [4] L. Beznea and N. Boboc: Potential Theory and Right Processes, Kluwer Acad. Publish., 2004.
• [5] N. Boboc and Gh. Bucur: “Excessive and supermedian functions with respect to subordinated resolvent of kernels”, Rev. Roum. Math. Pures et Appl., Vol. 39, (1994), pp. 875–878.
• [6] N. Boboc and Gh. Bucur: “Dilation operators in excessive structures; existence and uniqueness”, In: Potential Theory ICPT 94, Walter de Gruyter& Co, 1996, pp. 311–339.
• [7] J. Franchi and Y. Le Jan: “Sur les trajectoires intrinsèques des processus de Markov et le théorèm de Shih”, Ann. Inst. H. Poincaré Probab. Statist., Vol. 20, (1984), pp. 103–126.
• [8] P.A. Meyer: “Semi-groups en dualité”, In: Sém. de Th: du Potentiel (Brelot-Choquet-Deny) 5eannée: 1960/61, Vol. 10, Secrétariat math. Paris, 1961, p. 1–14.
• [9] P.A. Meyer: “Fonctionelles multiplicatives et additives de Markov”, Ann. Inst. Fourier (Grenoble), Vol. 12, (1962), pp. 125–230.
• [10] G. Mokobodzki: Operateur de subordination des resolventes, 1983, unpublished manuscript.
• [11] C.T. Shih: “Markov processus where hitting distributions are dominated by those of a given process”, Trans. Amer. Math. Soc., Vol. 129, (1967), pp. 157–179. http://dx.doi.org/10.2307/1994370

Identyfikatory

DOI

10.1007/s11533-005-0009-y